Related papers: Localization structure of electronic states in the…
The phenomenon of quantum antiresonance (QAR), i.e., exactly periodic recurrences in quantum dynamics, is studied in a large class of nonintegrable systems, the modulated kicked rotors (MKRs). It is shown that asymptotic exponential…
Quantum many-body systems pose a formidable computational challenge due to the exponential growth of their Hilbert space. While machine learning (ML) has shown promise as an alternative paradigm, most applications remain at the…
The quantum Hall ferromagnet at filling fraction $\nu = 1$ has some unusual properties due to the remarkable identity between the topological density of a spin distortion and the associated electrical charge density. We investigate the…
The quantum Hall effect hosts quantum phase transitions in which the localization length, that is the size of disorder-induced bulk localized states, is governed by universal scaling from percolation theory. However, this universal…
We study the real-space entanglement spectrum for fractional quantum Hall systems, which maintains locality along the spatial cut, and provide evidence that it possesses a scaling property. We also consider the closely-related particle…
Using scanning tunneling spectroscopy in ultra-high vacuum at low temperature (T = 0.3 K) and high magnetic fields (B < 12 T), we directly probe electronic wave functions across an integer quantum Hall transition. In accordance with…
The fractional quantum Hall (FQH) effect arises from strong electron correlations in a quantising magnetic field, and features exotic emergent phenomena such as electron fractionalisation. Using the diagrammatic Monte Carlo approach with…
We theoretically examine entanglement in fractional quantum hall states, explicitly taking into account and emphasizing the quasi-two-dimensional nature of experimental quantum Hall systems. In particular, we study the entanglement entropy…
The presence of disorder in semiconductors can dramatically change their physical properties. Yet, models faithfully accounting for it are still scarce and computationally inefficient. We present a mathematical and computational model able…
We report the consequences of a new interaction symmetry that protects the renormalization of the electron gas in low dimensions in general, and in the quantum Hall regime in particular. We introduce a generalized Thouless' criterion for…
A new type of localization - localization over the quantum resonance cells - in an intrinsically degenerate system is explored by using the quasienergy eigenstates.
We develop a microscopic theory of disorder-induced localization for a quantum particle moving in a fully ionized classical one-component plasma, within the static-fluctuation approximation. The random potential acting on the particle…
We investigate the effects of vacancies, disorder and sublattice polarization on the electronic properties of a monolayer graphene in the quantum Hall regime. Energy spectra as a function of magnetic field and the localization properties of…
The resistivity minima of the quantum Hall effect arise due to the localization of the electron states at the Fermi energy, when it is positioned between adjacent Landau levels. In this paper we calculate the localization length $\xi$ of…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
States of strongly interacting particles are of fundamental interest in physics, and can produce exotic emergent phenomena and topological structures. We consider here two-dimensional electrons in a magnetic field, and, departing from the…
When a system thermalizes it loses all local memory of its initial conditions. This is a general feature of open systems and is well described by equilibrium statistical mechanics. Even within a closed (or reversible) quantum system, where…
The problem of Bloch electrons in two dimensions subject to magnetic and intense electric fields is investigated, the quantum Hall conductance is calculated beyond the linear response approximation. Magnetic translations, electric evolution…
We introduce an efficient neural network (NN) architecture for classifying wave functions in terms of their localization. Our approach integrates a versatile quantum phase space parametrization leading to a custom 'quantum' NN, with the…
We have introduced a controllable nano-scale incursion into a potential barrier imposed across a two-dimensional electron gas, and report on the phenomena that we observe as the incursion develops. In the quantum Hall regime, the…